In a mixing bowl fitted with a dough hook, combine the flour, water, egg, fresh yeast, salt, sugar, and honey. Start the mixer on a medium-slow speed and mix until the ingredients form a smooth, homogeneous dough. Then, increase the speed to medium-high and continue mixing until the dough pulls away from the sides of the bowl. Add the "beurre pommade"** (see notes) and knead until the dough fully comes together. Cover the bowl with a damp cloth and let the dough rise at room temperature (75°F to 77°F) for 1 hour.
Once the dough has risen, gently press it down to release the air, then roll it out into a large rectangle that’s twice as long as the width of your "beurre de tourage." Place the dough in the freezer for 5 minutes, then transfer it to the refrigerator for 15 minutes. Next, place the "beurre de tourage" in the center of the dough, and fold the dough over from each side to completely cover the butter.
With the edge where the butter is visible facing you, use a rolling pin to make a double fold: roll from the bottom to the top until the dough is about 7 mm thick. Mark the middle of the dough, fold the top and bottom edges toward the center, then fold the dough in half again, like closing a wallet. Wrap the dough in plastic wrap and refrigerate it for 10 minutes.
For the final fold, roll the dough out to a thickness of 1 cm, forming a long rectangle. Fold the top third of the dough down over the middle third, then fold the bottom third up over the top. Roll out the dough to a thickness of 3.5 mm to begin cutting and shaping the croissants.